Structural damage detection based on stochastic subspace identification and statistical pattern recognition: I. Theory

Abstract

One of the key issues in vibration-based structural health monitoring is to extract the damage-sensitive but environment-insensitive features from sampled dynamic response measurements and to carry out the statistical analysis of these features for structural damage detection. A new damage feature is proposed in this paper by using the system matrices of the forward innovation model based on the covariance-driven stochastic subspace identification of a vibrating system. To overcome the variations of the system matrices, a non-singularity transposition matrix is introduced so that the system matrices are normalized to their standard forms. For reducing the effects of modeling errors, noise and environmental variations on measured structural responses, a statistical pattern recognition paradigm is incorporated into the proposed method. The Mahalanobis and Euclidean distance decision functions of the damage feature vector are adopted by defining a statistics-based damage index. The proposed structural damage detection method is verified against one numerical signal and two numerical beams. It is demonstrated that the proposed statistics-based damage index is sensitive to damage and shows some robustness to the noise and false estimation of the system ranks. The method is capable of locating damage of the beam structures under different types of excitations. The robustness of the proposed damage detection method to the variations in environmental temperature is further validated in a companion paper by a reinforced concrete beam tested in the laboratory and a full-scale arch bridge tested in the field.

Recent progress and future trends on damage identification methods for bridge structures

“…Comanducci et al conducted the vibration‐based damage detection using multivariate statistical techniques, and they used the concept of local principal component analysis, which allows one to overcome the assumption of linear correlation between output variables. Ren et al and Lin et al established a damage‐sensitive but environment‐insensitive damage index through the covariance‐driven identification based on the stochastic subspace together with the statistical pattern recognition technology; the damage index is insensitive to the temperature variation; numerical results show it can detect 20% stiffness reduction at a position near three‐fouth span of the first span of a continuous beam; moreover, the method proves capable of detecting 17% prestressed force loss in a laboratory prestressed reinforced concrete beam, as well as the damage supposed by the renewal stage change in a real box‐type reinforced concrete arch bridge under varying temperature.…”

Statics-Based Model-Free Damage Detection under Uncertainties Using Modal Interval Analysis

“…Due to this, probabilistic or nonprobabilistic theories should be involved in the damage detection process [5]. Probabilistic methods are mostly used with the aid of stochastic finite element algorithms [6], statistical pattern recognition [7] and Bayesian inference [8]. When sufficient statistical information on structural parameters and responses is not available or will incur high costs, uncertainty-based damage detection must rely on fuzzy theories [9,10] or interval analyses [11,12].…”

An iterative total least squares‐based estimation method for structural damage identification of 3D frame structures

“…Vibration‐based SHM methods can be classified into two classes: data‐driven approaches and physics‐based approaches . The former aims to assess variations in structural response measurements, but may be inefficient for predicting the nature and severity of the structural damage . On the other hand, physics‐based approaches—for example, finite element (FE) model updating methods—involve estimating or updating the parameters of a model so that the key model characteristics match those of the experimental structure .…”